How do illegal immigrants get into the European Union?

(CNN) — The death of more than 300 African migrants in a shipwreck off the Italian island of Lampedusa in early October has shone a spotlight on illegal immigration to Europe.

But although the tragedy at Lampedusa shocked the world, it has done little to dissuade migrants who continue to make the perilous journey across the Mediterranean from northern Africa to European shores.

Frontex, the European Union border agency, says the majority of people residing illegally in the EU arrived by plane with a valid travel visa and simply stayed on after their visa expired.

But Frontex also estimates that at least 72,000 people illegally entered the EU via land and sea routes in 2012 — and the actual figure may be much higher

According to Frontex’s “Annual Risk Analysis 2013” report, 51% of migrants entering illegally via land and sea took an eastern Mediterranean route, with many crossing into Greece before continuing on to the western Balkans by land or through ferry links to Italy.

While detections of illegal border crossings dropped in the western Mediterranean area between northern Africa and Spain, attempted migrant incursions through the central Mediterranean region — including Italy — are up in 2012, according to the report. Many of the migrants are fleeing violence and poverty in places like Syria and Libya.

The deaths of hundreds of migrants in early October has prompted EU leaders to review the bloc’s immigration policies.

The EU’s commissioner for home affairs, Cecilia Malmstrom, issued a statement in early October calling on European nations to give Frontex the resources to mount “a wide Frontex search and rescue operation in the Mediterranean, from Cyprus to Spain.”

The EU also said it is setting up a new border surveillance system and Mediterranean task force to bolster its efforts and will review its asylum immigration policies next summer.